Problem Statement

A sequence $B=(B_1,\ldots,B_N)$ of length $N$ consisting of integers between $1$ and $N$ (inclusive) is called a good sequence if and only if it satisfies the following condition:

• For every interval $[l,r]\ (1\leq l \leq r \leq N)$, there exists an integer $x\ (l\leq x\leq r)$ such that the following condition holds:
• Prepare a graph with $N$ vertices numbered from $1$ to $N$ and zero edges. For each $l \leq i \leq r$, if $i\neq x$, add an edge between vertices $i$ and $B_i$. Then, vertices $l, l+1,\ldots,r$ form a tree. That is, vertices $l, l+1,\ldots,r$ are connected.

You are given a sequence $A=(A_1,\ldots,A_N)$ where each element is either an integer between $1$ and $N$, or $-1$. Find the number, modulo $998244353$, of ways to replace the elements that are $-1$ in $A$ with integers between $1$ and $N$ such that $A$ becomes a good sequence.

Constraints

• All input values are integers.
• $1\leq N\leq 2\times 10^5$
• $1\leq A_i\leq N$ or $A_i=-1$

Input

The input is given from Standard Input in the following format:

N
A_1 \cdots A_N

Output

Output the number, modulo $998244353$, of ways to replace the elements that are $-1$ in $A$ with integers between $1$ and $N$ (inclusive) such that $A$ becomes a good sequence.